To summarize: there is a superhuman registration act. It is unclear exactly what it means to register, but it is being written as an attempt to create a superhero analogy to the Patriot Act and Guantanamo Bay (a summary here and here's a thread discussing it).

It bears some similarity to the earlier mutant registration act, but it seems Marvel is trying to sweep that under the rug and pretend this thing is completely new.

(Interestingly, it was casually mentioned in the comics that the NRA came out against the mutant registration act. They considered it similar to gun registration. I suspect that Marvel is going to studiously ignore any possibility that the NRA might join the side of right in this storyline.)

I don't find the arguments for applying the rational basis test versus compelling interest very compelling in this article. I kinda got the sense that he wanted the analysis to come out badly to use as a metaphor for what is happening today.

Still it's lots of fun. As a historical matter what have the courts done in equal protection cases where there is an objectively rational justification but the legislature was clearly motivated by simple dislike?

Xavier is quite inconsistent; Being integrated into society very much includes being equally subject to the laws as anyone else. But in the comics there have been numerous occations where he's sent out the X-Men to rescue/jailbreak/round up some random mutant who have just killed or injured non-mutants accidentally or in self defence.

Hello Professor X? Ever heard about Trials? Self defence is a much better defence than assault on officers and evading arrest, and even in cases of accidental killings with good lawyers they might get a suspended sentence on the condition that you keep them within arms reach and under control.

And the reaction on the depowering drug in the third movie seems to be "We are totally against its existence, it should never be used, except if we need to use ourselves against some villain, but the non-mutants shouldn't be allowed to have it!"
If they were integrated into society they'd talk about safeguards against wrongful depowering, keeping it "Safe, legal and rare" and so on.

Now the reason for this dissonance is that it is an Axiom of the X-Men that the authorities should be kept at arms length, since their Role is to be Outcasts and Rebels.
Unfortunately in practice it leads to Magneto talking about Mutant Sovereignity and practicing terror, and Xavier talking about integration and practicing Mutant Sovereignity.

On the subject of discrimination...how might mutants affect business antidiscrimination laws? I can think of one example: casinos will want to be able to legally turn away telekinetics - at craps, roulette, and other games involving moving parts - and telepaths - at poker (obviously) and blackjack (telepaths can read minds to learn other players' down cards). They can already discriminate against card counters, so the legal grounds for such would seem to be already in place.

But how would they detect telekinetics and telepaths? Most likely they'd need a finely-tuned version of Dr. Xavier's mutant-detecting device Cerebro, one that can spot the genes that cause the cheat-enabling mutations in question - something roughly analogous to security cameras. The device would have to have a much shorter range than Cerebro - on-premesis only - to saisfy privacy concerns.